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. 2022 Oct 30;41(24):4809-4821.
doi: 10.1002/sim.9537. Epub 2022 Aug 17.

Paired serial limiting dilution assays

Xiudi Li  1 , Susanne May  1 , Ilana M Trumble  2 , Nancie M Archin  3   4 , Michael G Hudgens  5
Affiliations

Paired serial limiting dilution assays

Xiudi Li et al. Stat Med. .

Abstract

Serial limiting dilution (SLD) assays are a widely used tool in many areas of public health research to measure the concentration of target entities. This concentration can be estimated via maximum likelihood. Asymptotic as well as exact inference methods have been proposed for hypothesis testing and confidence interval construction in this one-sample problem. However, in many scientific applications, it may be of interest to compare the concentration of target entities between a pair of samples and construct valid confidence intervals for the difference in concentrations. In this paper, an exact, computationally efficient inferential procedure is proposed for hypothesis testing and confidence interval construction in the two-sample SLD assay problem. The proposed exact method is compared to an approach based on asymptotic approximations in simulation studies. The methods are illustrated using data from the University of North Carolina HIV Cure Center.

Keywords: HIV-AIDS; exact methods; serial limiting dilution assays.

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Conflict of interest statement

Conflict of Interest: None declared.

Figures

FIGURE 1
FIGURE 1
Example of paired serial limiting dilution assays. Each sample is analyzed using 6 dilution levels and 2 replicates per dilution level. + indicates that the well tests positive (the target entity is present); − indicates that the well tests negative (the target entity is not present). The vector xi denotes the total number of positive wells at each dilution level for sample i.
FIGURE 2
FIGURE 2
Proposed exact inference procedure for the difference in IUPM Δ = τ1 − τ2, in the two-sample SLD assay problem. The upper shaded box corresponds to the pre-processing step, which can be performed given the experiment setting alone and before the assay outcome is observed; the lower shaded box corresponds to an exact test for a particular null hypothesis. Boxes correspond to required calculations or actions, and ovals correspond to the input and output of these actions. Abbreviations and notation as in Table 1.
FIGURE 3
FIGURE 3
Maximum likelihood estimate, E (estimate) approach confidence interval (CI) and asymptotic (A) CI for the difference in IUPM (infectious units per million) τvor − τctrl, where τvor denotes the IUPM from VOR (vorinostat) stimulated cultures and τctrl denotes the IUPM from control cultures, for samples from 16 individuals living with HIV (human immunodeficiency virus).
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